21. Number Theory -- From Wolfram MathWorld number theory is a vast and fascinating field of mathematics, sometimes called higher arithmetic, consisting of the study of the properties of whole http://mathworld.wolfram.com/NumberTheory.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... General Number Theory Number Theory Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and prime factorization are especially important in number theory, as are a number of functions such as the divisor function Riemann zeta function , and totient function . Excellent introductions to number theory may be found in Ore (1988) and Beiler (1966). The classic history on the subject (now slightly dated) is that of Dickson (1952). The great difficulty in proving relatively simple results in number theory prompted no less an authority than Gauss to remark that "it is just this which gives the higher arithmetic that magical charm which has made it the favorite science of the greatest mathematicians, not to mention its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics." Gauss, often known as the "prince of mathematics," called mathematics the "queen of the sciences" and considered number theory the "queen of mathematics" (Beiler 1966, Goldman 1997). SEE ALSO: Abstract Algebra Additive Number Theory Algebraic Number Theory Analytic Number Theory ... Totient Function REFERENCES: Andrews, G. E.

22. INTEGERS: The Electronic Journal Of Combinatorial Number Theory The proceedings for the Integers Conference 2005 (Volume 7(2)) have been published by de Gruyter as Combinatorial number theory In Celebration of the 70th http://www.integers-ejcnt.org/

Editorial board Author index Subscribe News The last Integers Conference took place October 24-27, 2007, at The University of West Georgia. The conference website is here The proceedings for the Integers Conference 2005 ( Volume ) have been published by de Gruyter as "Combinatorial Number Theory: In Celebration of the 70th Birthday of Ronald Graham." Current and Recent Volumes Volume Volume Proceedings of Integers Conference 2005 in Honor of Ron Graham's Birthday Volume All Volumes Instructions for Authors Download statistics INTEGERS is a refereed electronic journal devoted to research in the area of combinatorial number theory. It is published with the help of the University of West Georgia, Charles University, and DIMATIA. Subscriptions to INTEGERS are free. We welcome original research articles in combinatorics and number theory, with a preference for those that have a connection to both fields. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. The principal subject areas, according to the American Mathematical Society subject classification scheme are 05A, 05C55, 05C65, 05D, 11A, 11B, 11K, 11N, 11P, 11Y, and 91A46. INTEGERS also houses a combinatorial games section. ISSN 1553-1732

23. Mathematics Disclaimer number theory Web. The main site is in Vancouver, as of 31st May 2003. Last modified 10th January 2005. http://www.maths.uq.edu.au/~krm/ntw/

Mathematics All of UQ Select a quick link: Other Mathematics Links MathSciNet School of Physical Sciences Faculty of EPSA About UQ my.UQ mySI-net Programs and Courses UQ News UQ Experts UQ Images Organisational Units Staff Web Page You have requested the document http://www.maths.uq.edu.au/~krm/ntw/ . This is a staff web area hosted on a University of Queensland web server. Please be advised that the web pages within this area are NOT officially endorsed by The University of Queensland. The University accepts no responsibility or liability for the contents of this area. This message has been displayed in accordance with the University's Internet Code of Practice , which forms a part of the Please note that you will need to enable cookies in your browser in order to proceed. to continue, or to the Mathematics home page. privacy feedback © 2004 The University of Queensland, Brisbane, Australia ABN 63 942 912 684 CRICOS Provider No: Authorised by: Head of School Maintained by: webmaster@sps.uq.edu.au Last Updated - Today 09:31pm

24. Number Theory - Wikibooks, Collection Of Open-content Textbooks This book covers an elementary introduction to number theory, with an emphasis on presenting and proving a large number of theorems. http://en.wikibooks.org/wiki/Number_Theory

Number Theory From Wikibooks, the open-content textbooks collection Jump to: navigation search edit Elementary Number Theory This book covers an elementary introduction to Number Theory, with an emphasis on presenting and proving a large number of theorems. No attempts will be made to derive number theory from set theory and no knowledge of Calculus will be assumed. It is important to convince yourself of the truth of each proof as you work through the book, and make sure you have a complete understanding. For those who wish to use this as a reference book, an index of theorems will be given. edit Chapters Notation and Introduction to proof Elementary Divisibility Unique Factorization Congruences ... edit See also Proofs in Number Theory Retrieved from " http://en.wikibooks.org/wiki/Number_Theory Subjects Number Theory Mathematics ... Math for university Views Book Discussion Edit this page History Personal tools Log in / create account Navigation Main Page Help Cookbook Wikijunior ... Donations Community Bulletin Board Community portal Reading room Help cleanup ... Contact us Search Toolbox What links here Related changes Upload file Special pages ... Permanent link In other languages Portuguªs This page was last modified 22:22, 11 February 2008.

25. Basics Of Computational Number Theory Notes and Javascript illustrations by Robert Campbell. http://www.math.umbc.edu/~campbell/NumbThy/Class/BasicNumbThy.html

Basics of Computational Number Theory Robert Campbell Contents Introduction Modular Arithmetic GCD - The Euclidean Algorithm Exponentiation - The Russian Peasant Algorithm ... Galois Fields Appendices Programming Notes References Glossary Introduction This document is a gentle introduction to computational number theory. The plan of the paper is to first give a quick overview of arithmetic in the modular integers. Throughout, we will emphasize computation and practical results rather than delving into the why. Simple programs, generally in JavaScript, are available for all of the algorithms mentioned. At the end of the paper we will introduce a the Gaussian Integers and Galois Fields and compare them to the modular integers. Companion papers will examine number theory from a more advanced perspective. Modular Arithmetic Modular arithmetic is arithmetic using integers modulo some fixed integer N . Thus, some examples of operations modulo 12 are: 7 + 7 = 14 = 2 (mod 12) 5 * 7 = 35 = 11 (mod 12) Further examples can be generated and checked out with the following short programs. Note that, as JavaScript cannot compute with integers larger than 20 digits, the largest modulus allowed is 10 digits. (mod (mod Among the basic operations we have missed the division operator. If we were working in the integers we would almost never be able to define a quotient (unless the answer is itself an integer). In the modular integers we can often, but not always, define a quotient:

26. Number Theory | Mathematical Institute - University Of Oxford number theory Group. Members, publications, meetings. http://www.maths.ox.ac.uk/ntg/

@import "/modules/aggregator/aggregator.css"; @import "/modules/node/node.css"; @import "/modules/system/defaults.css"; @import "/modules/system/system.css"; @import "/modules/user/user.css"; @import "/./sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/cck/content.css"; @import "/sites/all/modules/drutex/drutex.css"; @import "/sites/all/modules/event/event.css"; @import "/sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/date/date.css"; @import "/sites/all/modules/cck/fieldgroup.css"; @import "/sites/all/modules/devel/devel.css"; @import "/sites/all/themes/maths/style.css"; Skip navigation Locator: Home » Number Theory Number Theory Home Contact Us Research Groups Analytic Topology Combinatorics Number Theory Members ... Research Information for: Prospective Students Current Students Teaching Staff Information about: People Research Events Notices ... About Us Departmental Members Login Username: Password: OU Webauth (Undergraduates) General information Members of the research group The number theory mailing list Research Preprints by members of the research group Rational Points on Algebraic Varieties (EPSRC grant no. GR/R93155/01)

27. Journal Of Number Theory | Department Of Mathematics The Journal of number theory was founded at The Ohio State University in 1969 by Professors R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus. http://www.math.ohio-state.edu/JNT/

@import "/misc/drupal.css"; @import "/modules/acidfree/acidfree.css"; @import "/themes/osumath/style.css"; @import "/modules/codefilter/codefilter.css"; @import "/modules/event/event.css"; @import "/modules/img_assist/img_assist.css"; @import "/modules/quote/quote.css"; @import "/modules/rsvp/rsvp.css"; @import "/modules/tables/tables.css"; @import "/modules/devel/devel.css"; @import "/modules/tinymce/upload_image/upload_image.css"; @import "/themes/osumath/navbar.css"; Begin OSU masthead and toolbar The Ohio State University www.osu.edu OSU Help Campus map ... Home Journal of Number Theory The Journal of Number Theory was founded at The Ohio State University in 1969 by Professors R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus. Editor-in-Chief: David Goss For more information, including a list of editorial board members and author instructions, please see Elsevier To submit to JNT, please go to http://ees.elsevier.com/jnt/ Office Susan Hunter Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, Ohio 43210-1174

28. Algebra And Number Theory Journal Editorial Board About ANT Submission Subscription Contents Editors Addresses Interests The Journal Scientific Advantages Contacts http://pjm.math.berkeley.edu/ant/about/cover/cover.html

// Javascript Editorial Board About ANT Submission Subscription ... Current Issue

29. International Journal Of Number Theory (World Scientific) Original research papers and review articles on all areas of number theory. http://www.worldscinet.com/ijnt/ijnt.shtml

30. The Number Theory Group At UCLA number theory Group. Members, events, resources. http://www.math.ucla.edu/~ntg/

UCLA Number Theory Group Announcements Seminar People Courses ... Links UCLA has a well-established research group in Number Theory. The group is led by 5 core faculty members, and currently has 5 post-doctoral members. Numerous graduate students, at all stages of their education, actively participate in the courses and seminars of the group. Additionally, a number of UCLA faculty members specialize in closely affiliated areas, such as K-theory, quadratic forms, additive combinatorics, and cryptography. Announcements Back to top Jan 6, 2008 - UCLA Spotlight on Craig Citro. Nov 25, 2007 - Chandrashekhar Khare was awarded the 2007 Fermat Prize Nov 15, 2007 - Recent Developments in Number Theory: Selmer Groups, L-functions, and Galois Deformations is an upcoming conference to be held here at UCLA in the spring (during spring break) of 2008. The webpage is now up make sure to spread the word! (There is funding for grad students and young researchers to attend, so make sure to spread the word to friends at other universities, too.) Sep 21, 2007 - Welcome back!

31. Archives Of NMBRTHRY@LISTSERV.NODAK.EDU Archives of postings to the number theory mailing list (NMBRTHRY). http://listserv.nodak.edu/archives/nmbrthry.html

List Archives Subscriber's Corner Server Archives List Archives List Management List Moderation Server Management Help ... Archive Search Archives of NMBRTHRY@LISTSERV.NODAK.EDU Number Theory List Search the archives Post to the list Join or leave the list (or change settings) Manage the list (list owners only) March 2008 February 2008 January 2008 November 2007 ... LISTSERV.NODAK.EDU

32. Elementary Number Theory This is a textbook about prime numbers, congruences, basic publickey cryptography, quadratic reciprocity, continued fractions, elliptic curves, and number http://modular.math.washington.edu/ent/

Elementary Number Theory William Stein Intended for Publication by Springer-Verlag September 2004 This is a textbook about prime numbers, congruences, basic public-key cryptography, quadratic reciprocity, continued fractions, elliptic curves, and number theory algorithms. We assume the reader has some familiarity with groups, rings, and fields, and some programming experience. This book grew out of an undergraduate course that the author taught at Harvard University in 2001 and 2002. Download: Feel free to download this book and send me feedback , so the published version will be better. ent.pdf PDF version (1.6MB) ent.ps : Postscript version (9.2MB) ent.dvi : DVI version (1.1MB, missing diagrams and photos) : Python source code for Chapter 7 (download and rename to ent.py

33. International Press: Communications In Number Theory And Physics A publication of the International Press, publishing papers on all areas in which number theory and physics interact with each other. http://www.intlpress.com/CNTP/

International Press Home About Journals Books ... Contact Us Journals AJM Asian Journal of Mathematics ATMP Advances in Theoretical and Mathematical Physics ... Statistics and Its Interface Journals Communications in Number Theory and Physics Communications in Number Theory and Physics Editors: R. Dijkgraaf, D. Kazhdan, M. Kontsevich, and S.-T. Yau ISSN: 1931-4523 (print); 1931-4531 (online) Issues: 4/year Aims and Scope: Communications in Number Theory and Physics is an international journal focused on applications of Number Theory in the broadest sense to Theoretical Physics. The journal offers a forum for communication among researchers in Number Theory and Theoretical Physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields. Browse Journal Editorial Board Submissions Subscribe/Renew The journal covers the following areas of research: Number Theory: Analytic Number Theory Arithmetic and Algebraic Geometry Computational and Experimental Number Theory Differential Equations Modular and Automorphic Forms Motives Non-commutative Geometry Transcendental Methods Applications of these methods to Theoretical Physics: Conformal Field Theory Topological Field Theory Quantum Field Theory Feynman Path Integrals and Evaluation of Feynman Graphs Mirror Symmetry String Theory Readership In recent years, the world has seen explosive interactions between Number Theory, Arithmetic Geometry and Theoretical Physics, particularly in String Theory. To name a few examples, modular and quasi-modular forms appear in many areas in Physics - e.g., mirror symmetry, Gromov-Witten invariants, Calabi-Yaus. Also, modularity questions of Calabi-Yau varieties and higher-dimensional varieties in connection with the Langlands Program are receiving considerable attention and feedback from the physics fields. Via renormalization, Feynman integrals are related to multiple zeta-values, and purportedly to motives. The zeta-functions and L-series appear in many works in the liturature of physics.

34. Number Theory Foundation Private philanthropic US organization for research in number theory. http://homes.cerias.purdue.edu/~ssw/ntf/

Number Theory Foundation The NTF pages have been moved to the University of Illinois. Please change your link to "http://www.math.uiuc.edu/ntf/": The new Number Theory Foundation web page.

35. Number Theory Index History Topics Numbers and number theory Index. Number systems in ancient civilisations, Other number theory. Arabic number systems http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Number_Theory.html

History Topics: Numbers and Number Theory Index Number systems in ancient civilisations Other number theory Arabic number systems Babylonian number systems Egyptian number systems Greek number systems ... Search Form JOC/EFR September 2007 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Number_Theory.html

36. Math 259: Introduction To Analytic Number Theory (Spring 1998) Lecture notes for Math 259 Introduction to Analytic number theory (Spring 1998). If you find a mistake, omission, etc., please let me know by email. http://www.math.harvard.edu/~elkies/M259.98/index.html

Lecture notes for Math 259: Introduction to Analytic Number Theory (Spring 1998) If you find a mistake, omission, etc., please let me know by e-mail. The orange ball marks our current location in the course. For an explanation of the background pattern, skip ahead to the end of the page. plan.ps and intro.ps : administrivia and philosophy/examples elem.ps : Elementary methods I: variations on Euclid euler.ps : Elementary methods II: The Euler product for s>1 and consequences dirichlet.ps : Dirichlet characters and L-series; Dirichlet's theorem modulo the non-vanishing of L-series at s=1 chebi.ps click here For Erdos' simplification of Cebysev's proof of the "Bertrand Postulate": there exists a prime between x and 2x for all x>1. Adapted from Hardy and Wright, pages 343-344. psi.ps zeta1.ps gamma.ps prod.ps : Functions of finite order: Hadamard's product formula and its logarithmic derivative zeta2.ps free.ps pnt.ps : Conclusion of the proof of the Prime Number Theorem with error bound; some consequences and equivalents of the Riemann Hypothesis. Here's a bibliography lsx.ps

37. Number Theory And Physics Archive This website is an attempt to document in detail the rapidly emerging connections between physics and number theory. http://www.maths.ex.ac.uk/~mwatkins/zeta/physics.htm

number theory and physics archive introduction tutorial mystery new ... Communications in Number Theory and Physics (new journal) a message about the future of this website

38. London Number Theory Seminar Weekly meetings during term, rotating between University College, King s College and Imperial College. http://www.mth.kcl.ac.uk/events/numbtheo.html

London Number Theory Seminar The London Number Theory Seminar is held weekly during term times. The site rotates between KCL, Imperial College and UCL. This term, the seminar will be hosted by University College and will be held on Wednesdays from 4 pm to 5 pm, in room 707 of the UCL Math building on Gordon street. This term's organiser is Minhyong Kim. The seminar is preceded by a Study Group on arithmetic fundamental groups at 1 pm in the same room. The seminar will start on the 9th of January. LNTS Schedule 9 January Pierre Debes (Lille) "Inverse Galois theory, Abelian varieties and modular towers" 16 January Makis Dousmanis (Paris 13) "Reductions of some families of two-dimensional crystalline representations" 23 January Konstantin Ardakov (Nottingham) "Reflexive ideals in Iwasawa algebras" 30 January Ben Green (Cambridge) "Distribution of Polynomials over finite fields" We apply this result to the study of so-called Gowers norms. Let P : F^n -> F be any function. It is well-known that P is a polynomial of degree d if the polynomial Q obtained by differencing d+1 times is identically zero. What if Q is not identically zero, but merely biased towards zero? The inverse conjecture for the Gowers norms predicted that, in this case, P correlates with a degree d polynomial. Using the result described above we establish this in certain cases. We will also discuss an example which shows that the conjecture can fail in very low characteristic. Joint work with T. Tao.

39. Discovering Number Theory Discovering number theory. Jeffrey J. Holt, John W. Jones. University of Virginia, Arizona State University. Chapter 0. Introduction to Active Web Pages http://www.math.mtu.edu/mathlab/COURSES/holt/dnt/

Jeffrey J. Holt John W. Jones University of Virginia Arizona State University Chapter 0. Introduction to Active Web Pages Chapter 1. Divisibility and Factorization Chapter 2. The Euclidean Algorithm and Linear Diophantine Equations Chapter 3. Congruences ... Chapter 9. The Euler -function Chapter 10. Primitive Roots Chapter 11. Quadratic Congruences Chapter 12. Representation Problems Chapter 13. Continued Fractions

40. Math 254 (Number Theory) Lecture notes by Kiran Kedlaya, UC Berkeley, Spring 2002. http://www-math.mit.edu/~kedlaya/math254b.html

Math 254B (Number Theory) This was the official course web page for Math 254B (Number Theory) at UC Berkeley, which I taught during the Spring 2002 semester. The course web page for Math 254A, which I taught in Fall 2001, is here . Math 254B took a detailed look at class field theory, the theory of abelian extensions of number fields, which extends the reciprocity laws of Gauss, Legendre, Hilbert et al. Note added 9 Nov 2003: I am planning to leave these pages "as is" for now except for updating broken links and posting errata to the course notes in case anyone points them out. (These were largely corrected verbally in the lectures but I didn't put the changes into the notes.) In particular, the contact information for me is incorrect; see my home page for updated information. Stuff to download Note added 19 Jul 2002: all PostScript files are now compressed using gzip to save space. To decompress, type "gunzip blah.ps.gz"; your browser or PostScript viewer may do the decompression automatically. Course description and syllabus Lecture notes Final papers Current announcements The final papers are being posted here. If you want me to include yours, email me a copy in any format (except Word!).

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